Neural representations of absolute and relative magnitudes in symbolic and nonsymbolic formats

Abstract

Humans differ from other animal species in their unique ability to use symbols to represent numerical information. This ability is thought to emerge from the “neural recycling” of mechanisms supporting nonsymbolic magnitudes in the intraparietal sulcus (IPS), a hypothesis that has been applied to both absolute magnitudes (e.g., whole numbers) and relative magnitudes (e.g., fractions). Yet, evidence for the neuronal recycling hypothesis is inconsistent for absolute magnitudes and scarce for relative magnitudes. Here, we investigated to what extent the neural representations of absolute and relative magnitudes in symbolic and nonsymbolic formats overlap in the IPS. In a functional magnetic resonance imaging (fMRI) adaptation design, 48 adult participants were sequentially presented with lines, whole numbers, line ratios, and fractions that varied (vs. not varied) in magnitudes. Univariate analyses showed that the extent to which IPS mechanisms associated with whole numbers relied on mechanisms associated with lines depended upon participants’ arithmetic fluency. Multivariate analyses revealed that the right IPS encoded differences in format (nonsymbolic vs. symbolic) across both absolute and relative magnitudes. Therefore, IPS activity associated with magnitude processing may depend on the presentation format (nonsymbolic vs. symbolic) more than it depends on the type of magnitude (absolute vs. relative), at least for most adult participants.

Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age

“…Yet, a growing number of recent studies, also in adults, have failed to find such format invariance. Some have thus claimed that the link between symbolic and nonsymbolic representations might be more tenuous than previously thought [ 12 – 15 ]. Critically, our findings suggest that the representation of nonsymbolic quantity may still scaffold the acquisition of symbolic numerical skills in young children.…”

“…Cluster-wise p -values were calculated for each target actual cluster, based on the number of randomly generated clusters in which the cluster size was larger than the target cluster size, divided by the total number of randomly generated clusters. In line with our most recent fMRI study using multivariate analyses [ 15 ], the statistical threshold was set at p < 0.005 for the voxel level and at p < 0.05 for the cluster level. Additional control analyses, however, use a voxel level of p < 0.001 to ensure that this parameter does not critically affect our conclusions ( S13 Fig ).…”

“…However, a growing number of studies have also failed to find an overlapping neural activity for symbolic and nonsymbolic quantity processing [ 12 , 13 ]. For example, two recent reports have shown distinct neural representations of number symbols and nonsymbolic quantities across the largest samples of adult participants to date [ 14 , 15 ]. These studies suggest that quantity may be represented in a format-dependent manner in the brain [ 16 ].…”

“…To circumvent these issues, we used a block-design adaptation paradigm in which children were passively presented with blocks of nonsymbolic quantities (dot arrays) and Arabic numerals (digits) that were either similar (adaptation) or different (no-adaptation) ( Fig 1B ). Because the repeated presentation of a given stimulus leads to a decrease in activity in the region that processes that stimulus [ 23 ], comparing no-adaptation to adaptation blocks captures a neural adaptation effect in task-relevant regions [ 15 , 24 ].…”

Developmental Changes in Nonsymbolic and Symbolic Fractions Processing: A Cross-Sectional fMRI study

“…In contrast to the putative limitations of the ANS, a recent body of research has detailed a perceptual ability to process nonsymbolic fraction magnitudes, a type of nonsymbolic analog to symbolic fractions (e.g., Bhatia et al, 2020;Bhatia et al, 2022;Jacob & Nieder, 2009b;Jacob et al, 2012;Lewis et al, 2016;Matthews et al, 2016;Meng et al, 2019;Starling-Alves et al, 2022). Investigations centering this nonsymbolic ratio (henceforth called nonsymbolic fractions for simplicity) processing ability stand to expand the neuronal recycling hypothesis to the realm of fractions (Jacob et al, 2012;Lewis et al, 2016;Matthews et al, 2016;Sidney et al, 2017).…”